Motivated by applications in online advertising, we consider a class of maximization problems where the objective is function sequence actions and running duration each action. For these problems, introduce concepts sequence-submodularity sequence-monotonicity, which extend notions submodularity monotonicity from functions defined over sets to sequences. We establish that if sequence-submodular...

In this article, we study Hilbert Series of non-Cohen-Maculay tangent cones for some 4-generated pseudo symmetric monomial curves. We show that the Function is nondecreasing by explicitly computing it. also compute standard bases these toric ideals.

in this article, we verify existence and uniqueness of positive and nondecreasing solution for nonlinear boundary value problem of fractional differential equation in the form d_{0^{+}}^{alpha}x(t)+f(t,x(t))=0, 0x(0)= x'(0)=0, x'(1)=beta x(xi), where $d_{0^{+}}^{alpha}$ denotes the standard riemann-liouville fractional derivative, 0an illustrative example is also presented.

A renewal model in risk theory is considered, where H(u, y) is the tail of the distribution of the deficit at ruin with initial surplus u and F(y) is the tail of the ladder height distribution. Conditions are derived under which the ratio H(u, y)/F(u + y) is nondecreasing in u for any y ≥ 0. In particular, it is proven that if the ladder height distribution is stable and DFR or phase type, then...

We investigate the n-variable real functions G that are solutions of the Chisini functional equation F(x) = F(G(x), . . . , G(x)), where F is a given function of n real variables. We provide necessary and sufficient conditions on F for the existence and uniqueness of solutions. When F is nondecreasing in each variable, we show in a constructive way that if a solution exists then a nondecreasing...

The proof of the main result in Reny and Perry (2006) is provided here. We also provide an example in which the best reply to nondecreasing bidding functions fails to be nondecreasing, and we show how to approximate a degenerate density by one that satis…es the assumptions in Reny and Perry (2006). Finally, we establish that Reny and Perry’s (2006) main result continues to hold when the notion ...